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A304359 Antidiagonal sums of the second quadrant of array A(k,m) = F_k(m), F_k(m) being the k-th Fibonacci polynomial evaluated at m. 2
0, 1, 1, 1, 1, 1, 0, 2, 1, -10, 39, -58, -166, 1611, -6311, 10083, 54195, -565257, 2727568, -6102368, -26464605, 394614352, -2515452801, 8797315672, 11441288836, -458369484247, 4097437715969, -21769011878335, 36715605929957, 703213495381553, -10042075731879152 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
Equivalently, antidiagonal sums of the fourth quadrant of array A(k,m).
LINKS
FORMULA
a(n) = Sum_{j=0..n} F_j(j-n).
MAPLE
F:= (n, k)-> (<<0|1>, <1|k>>^n)[1, 2]:
a:= n-> add(F(-j, n-j), j=0..n):
seq(a(n), n=0..30);
# second Maple program:
F:= proc(n, k) option remember;
`if`(n<2, n, k*F(n-1, k)+F(n-2, k))
end:
a:= n-> add(F(j, j-n), j=0..n):
seq(a(n), n=0..30);
# third Maple program:
a:= n-> add(combinat[fibonacci](j, j-n), j=0..n):
seq(a(n), n=0..30);
MATHEMATICA
a[n_] := Sum[Fibonacci[j, j - n], {j, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 02 2018, from 3rd Maple program *)
CROSSREFS
Sequence in context: A071926 A133103 A336729 * A054781 A213421 A370068
KEYWORD
sign
AUTHOR
Alois P. Heinz, May 11 2018
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)